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Why Do Investors Over Pay For Junk Bonds?

|Includes: AGG, BND, BOND, HYG, SPDR Bloomberg Barclays High Yield Bond ETF (JNK)


One of the most curious financial markets phenomena is the fact that the credit spreads on highly distressed credits are lower than average compared to the matched maturity default probabilities for the issuer. The graph above shows clearly that the ratio of credit spread to default probability for the highest default risk issuers is well below the average on all heavily traded bonds, as measured by the black line in the graph. Investors would gain much more credit spread per basis point of default risk by buying higher quality, lower default probability issuers. The fact that this phenomenon exists is consistent with the equity market findings of Campbell, Hilscher, and Szilagyi (2008,2011). They showed that high default probability equities under-performed the equities of lower default probabiility firms by all risk-adjusted measures tested. These strange risk-return trade-offs are similar to the "lottery ticket phenomenon" in which individuals spend a dollar on a lottery ticket that on average will return $0.70 but which has a very slight chance of a huge pay-off.

Background on the Calculations

The chart shows the credit spread to default probability ratio on all corporate bond trades in the U.S. market which met the following conditions:

Coupon: Constant fixed rate until maturity

Maturity: 1 year or more

Trade volume: $5 million or more

Seniority: Senior debt

Callability: Non-call (except for "make whole" calls)

Survivor Option: Excluded

The credit spread is calculated by comparing the trade-weighted average yield to the matched maturity U.S. Treasury rate supplied by the U.S. Department of the Treasury to the Federal Reserve H15 statistical release. Calculations are by Kamakura Risk Information Services using data from TRACE. In a recent note, we explained why it is incorrect to use the common financial relationship that says credit spreads equal the default probability times (one minus the recovery rate). The graph above is additional evidence that this simple formula is incorrect. For more information please contact

Background on the Default Probability Models Used

The Kamakura Risk Information Services version 5.0 Jarrow-Chava reduced form default probability model (abbreviated KDP-JC5) makes default predictions using a sophisticated combination of financial ratios, stock price history, and macro-economic factors. The version 5.0 model was estimated over the period from 1990 to 2008, and includes the insights of the worst part of the recent credit crisis. Kamakura default probabilities are based on 1.76 million observations and more than 2000 defaults. The term structure of default is constructed by using a related series of econometric relationships estimated on this data base. KRIS covers 35,000 firms in 61 countries, updated daily. Free trials are available at An overview of the full suite of Kamakura default probability models is available here.

General Background on Reduced Form Models

For a general introduction to reduced form credit models, Hilscher, Jarrow and van Deventer (2008) is a good place to begin. Hilscher and Wilson (2013) have shown that reduced form default probabilities are more accurate than legacy credit ratings by a substantial amount. Van Deventer (2012) explains the benefits and the process for replacing legacy credit ratings with reduced form default probabilities in the credit risk management process. The theoretical basis for reduced form credit models was established by Jarrow and Turnbull (1995) and extended by Jarrow (2001). Shumway (2001) was one of the first researchers to employ logistic regression to estimate reduced form default probabilities. Chava and Jarrow (2004) applied logistic regression to a monthly database of public firms. Campbell, Hilscher and Szilagyi (2008) demonstrated that the reduced form approach to default modeling was substantially more accurate than the Merton model of risky debt. Bharath and Shumway (2008), working completely independently, reached the same conclusions. A follow-on paper by Campbell, Hilscher and Szilagyi (2011) confirmed their earlier conclusions in a paper that was awarded the Markowitz Prize for best paper in the Journal of Investment Management by a judging panel that included Prof. Robert Merton.

Disclosure: The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.